How to move modifiers of multiple objects up or down?
Override the context by passing the actual object {'object': obj} to bpy.ops.object.modifier_move_up() or  bpy.ops.object.modifier_move_down() operator. 

Example on how to move all subdivision modifiers by name (they are usually called 'Subdivision') of multiple objects to the top (position 0) in the modifier stack:

C = bpy.context
mod_name = "Subdivision"

for obj in C.selected_editable_objects:
    # Test whether there is a modifier called "Subdivision" at all 
    if any(m for m in obj.modifiers if m.name == mod_name):
        # Iterate through all modifiers in reverse
        for mod in reversed(C.object.modifiers):
            # Move the modifier as long as its position is 0
            while obj.modifiers.find(mod_name) != 0:
                bpy.ops.object.modifier_move_up({'object': obj}, modifier=mod_name)


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Move modifier to the top of the stack through python?
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